+131 If \(f(x) = x^2 - 3x + 4\), find the value of \(f(\sqrt3 - \sqrt2)\)
We have that f(x) = x^2 - 3x + 4. To find the value of f(sqrt(3) - sqrt(2)), we simply substitute sqrt(3) - sqrt(2) into the function for x. This gives us:
f(sqrt(3) - sqrt(2)) = (sqrt(3) - sqrt(2))^2 - 3(sqrt(3) - sqrt(2)) + 4
We can simplify this expression as follows:
= 3 - 3sqrt(2) + 3 - 3sqrt(3) + 4 = 10 - 3sqrt(2) - 3sqrt(3)
Therefore, the value of f(sqrt(3) - sqrt(2)) is 10 - 3sqrt(2) - 3sqrt(3).
Answer:
The value of f(sqrt(3) - sqrt(2)) is 10 - 3sqrt(2) - 3sqrt(3).
